Third-Moment Standardization for Structural Reliability Analysis
Publication: Journal of Structural Engineering
Volume 126, Issue 6
Abstract
First- and second-order reliability methods are generally considered to be among the most useful for computing structural reliability. In these methods, the uncertainties included in resistances and loads are generally expressed as continuous random variables that have a known cumulative distribution function. The Rosenblatt transformation is a fundamental requirement for structural reliability analysis. However, in practical applications, the cumulative distribution functions of some random variables are unknown, and the probabilistic characteristics of these variables may be expressed using only statistical moments. In the present study, a structural reliability analysis method with inclusion of random variables with unknown cumulative distribution functions is suggested. Normal transformation methods that make use of high-order moments are investigated, and an accurate third-moment standardization function is proposed. Using the proposed method, the normal transformation for random variables with unknown cumulative distribution functions can be realized without using the Rosenblatt transformation. Through the numerical examples presented, the proposed method is found to be sufficiently accurate to include the random variables with unknown cumulative distribution functions in the first- and second-order reliability analyses with little extra computational effort.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ang, A. H.-S., and Cornell, C. A. (1974). “Reliability basis of structural safety and design.”J. Struct. Div., ASCE, 100(9), 1755–1769.
2.
Ang, A. H.-S., and Tang, W. H. (1984). Probability concepts in engineering planning and design, Vol. II: Decision, Risk, and Reliability, Wiley, New York.
3.
Bjerager, P. ( 1991). “Methods for structural reliability computation.” Reliability problems: General principles and applications in mechanics of solids and structures, F. Casciati, ed., Springer, New York, 89–136.
4.
Breitung, K. (1984). “Asymptotic approximation for multinormal integrals.”J. Engrg. Mech., ASCE, 110(3), 357–366.
5.
Cai, G. Q., and Elishakoff, I. (1994). “Refined second-order reliability analysis.” Struct. Safety, Amsterdam, 14(3), 267–276.
6.
Der Kiureghian, A. (1989). “Measures of structural safety under imperfect states of knowledge.”J. Struct. Engrg., ASCE, 115(5), 1119–1140.
7.
Der Kiureghian, A., and De Stefano, M. (1991). “Efficient algorithm for second-order reliability analysis.”J. Engrg. Mech., ASCE, 117(12), 2904–2923.
8.
Der Kiureghian, A., Lin, H. Z., and Hwang, S. J. (1987). “Second-order reliability approximations.”J. Engrg. Mech., ASCE, 113(8), 1208–1225.
9.
Der Kiureghian, A., and Liu, P. L. (1986). “Structural reliability under incomplete probability information.”J. Engrg. Mech., ASCE, 112(1), 85–104.
10.
Ditlevsen, O. (1979). “Generalized second-moment reliability index.” J. Struct. Mech., 7(4), 435–451.
11.
Fu, G. K. (1994). “Variance reduction by truncated multimodal importance sampling.” Struct. Safety, Amsterdam, 13(3), 267–283.
12.
Hasofer, A. M., and Lind, N. C. (1974). “Exact and invariant second-moment code format.”J. Engrg. Mech. Div., ASCE, 100(1), 111–121.
13.
Hohenbichler, M., and Rackwitz, R. (1981). “Non-normal dependent vectors in structural safety.”J. Engrg. Mech., ASCE, 107(6), 1227–1238.
14.
Liu, Y. W., and Moses, F. (1994). “A sequential response surface method and its application in the reliability analysis of aircraft structural systems.” Struct. Safety, Amsterdam, 16(1), 39–46.
15.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety. Prentice-Hall, Englewood Cliffs, N.J.
16.
Melchers, R. E. (1990). “Radial importance sampling for structural reliability.”J. Engrg. Mech., 116(1).
17.
Ono, T., and Idota, H. (1986). “Proposal of the high order moment standardizing method and definition of reliability index.” J. Struct. and Constr. Engrg., Tokyo, 359, 43–49 (in Japanese).
18.
Rackwitz, R. (1976). “Practical probabilistic approach to design.” First order reliability concepts for design codes, Bull. d'Information, No. 112, Comite European du Beton, Munich, Germany.
19.
Rajashekhar, M. R., and Ellingwood, B. R. (1993). “A new look at the response surface approach for reliability analysis.” Struct. Safety, Amsterdam, 12(2), 205–220.
20.
Shinozuka, M. (1983). “Basic analysis of structural safety.”J. Struct. Engrg., ASCE, 109(3), 721–740.
21.
Stuart, A., and Ord, J. K. (1987). Kendall's advanced theory of statistics, Vol. 1, Distribution theory, 5th Ed., Charles Griffin, London.
22.
Tichy, M. (1994). “First-order third-moment reliability method.” Struct. Safety, Amsterdam, 16(2), 189–200.
23.
Winterstein, S. (1985). “Non-normal responses and fatigue damage.”J. Engrg. Mech., ASCE, 111(10), 1291–1295.
24.
Winterstein, S., and Bjerager, P. (1987). “The use of higher moments in reliability estimation.” Proc., Int. Conf. on Application of Statistics and Probability, Vancouver, Canada, Vol. 2, 1027–1036.
25.
Withers, C. S. (1984). “Asymptotic expansions for distributions and quantiles with power series cumulants.” J. Royal Statistical Soc., Series B, London, 46(3), 389–396.
26.
Zhao, Y. G., and Ono, T. (1999a). “New approximations for SORM: Part II.”J. Engrg. Mech., ASCE, 125(1), 86–93.
27.
Zhao, Y. G., and Ono, T. (1999b). “Response uncertainty and time-variant reliability analysis for hysteretic MDF structures.” Earthquake Engrg. and Struct. Dyn., 28, 1187–1213.
28.
Zong, Z., and Lam, K. Y. (1998). “Estimation of complicated distributions using B-spline functions.” Struct. Safety, Amsterdam, 20(4), 341–355.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 126 • Issue 6 • June 2000
Pages: 724 - 732
History
Received: Jun 16, 1999
Published online: Jun 1, 2000
Published in print: Jun 2000
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.